Who's the biggest influence on how the Beatles created their sound in your opinion?

Producer George Martin. He made it happen.

George Martin

There is no obvious overall influence like, say, Duran Duran with Roxy Music, where it really hits you in the face.

In the Fabs music, I hear: Everly Brothers, Chuck Berry, Buddy Holly, and Smokey Robinson. I also hear a bit of 50s rockabilly and the Beach Boys(Paperback Writer, If I Needed Someone, Because, etc.) But as many have pointed out, without George Martin to translate their sound to tape/disc, it just would not have happened, at least not as well as it did.

Sir George Martin.

George Martin and his expertise in studio recordings

I tend to think it was the fact that they were not musically trained then you add all that was [i]happening[/i] around them musically. Then add a dash of genius which just can' t be captured in words or put in a bottle.

And don't forget a few months playing up to 8 hours a night in the Red Light district of Hamburg.

Many many many! I couldn’t really say one was the most influential, and all 4 members (during their peak times) brought their own set of influences to the table. Frank Sinatra influenced McCartney’s vocal style, but so did Otis Redding. Ravi Shankar had a big influence on George Harrison as well as other musicians from India, and so did Carl Perkins. John Lennon was influenced by a lot of folk artists, and not just Bob Dylan but Dylan’s influences. Bach, people don’t know this in general but Denny Laine influenced both John and Paul. There’s way more.

Buddy Holly
Elvis Presley
People like that.

50's Rock n Roll influenced an entire generation of musicians

Little Richard, Buddy Holly, Elvis, Eddie Cochran, Chuck Berry, among others.

George Martin let them experiment and was able to bring in classical instruments and do those arrangements.

The Liverpool police department

Little Richard,Carl Perkins,Elvis,Chuck Berry..and many many others influenced their early sound.
Dylan,The Byrds,LSD,Marijuana,Eastern philosophy,George Martin..and once again..many many others for their mid to end of 60s influences.

[b]They[/b] credited a lot of U.S. influences, including black R&B and blues artists.

I hear so many different ones.
Elvis
English steet buskers
20s and 30s music
classical music

I can't limit to just one

The Lennon /McCartney writing collaboration. One had an idea and the other then finished it.

Elvis, Chuck Berry, Mississippi blues... just like all other Euro rockers of their time

Hits. They wanted hit records and became very good at making them

And they in turn influenced practically every other band since.

Jimminy Cricket?

Just let it be ..

George Martin

Other beetles

Elvis

Me

Me

Miley cyrus

Depends if you mean when they were good or when they went full hipster Fancy Lads?